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Function as a set of ordered pairs Let A and B be two non-empty sets. A relation f from A to B i.e a subset of A × B is called a function (or a mapping or a map) from A to B, if i) for each a ∈ A there exists b ∈ B…
Theorem 3 The total number of subsets of a finite set containing n elements is 2ⁿ. Proof Let A be a finite set containing n elements.Let 0 ≤ r ≤ n. Consider those subset,of A that have r elements each.We know that the number of ways in which r elements can be chosen…
Pressure The molecules of a gas are in random motion. The rapidly moving molecules continually impact on the surface of the container and its effect is to produce a force over the surface. The force normal to unit area of surface is called pressure acting on the surface. The normal force exerted by the atmosphere…
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Subsets of the set R of real numbers Following sets are important subsets of the set R of all real numbers: (i) The set of all natural numbers N = { 1, 2, 3, 4, 5, 6,…. } (u) The set of all integers Z = { … – 3, – 2, -1,…
Thermodynamic system Thermodynamic system is defined as quantity of matter or a region in a space chosen for study. Everything external to the system is called surroundings. The system is separated from the surroundings by the boundary that may be real or imaginary The boundary does not intervene between the system and surroundings. It only…
